Chapter 12

Lauren Wible of Bucknell University was the 2005 NCAA Division I women's softball batting leader with a batting average of .524. This means that the probability of her getting a hit in a given at-bat was \(0.524 .\) Find the probability of her getting 4 hits in 4 at-bats.

For Exercises \(5-8,\) use the following information. The useful life of a certain car battery is normally distributed with a mean of \(100,000\) miles and a standard deviation of \(10,000\) miles. The company makes \(20,000\) batteries a month. About how many batteries will last less than \(90,000\) miles?

Find the variance and standard deviation of each set of data to the nearest tenth. {5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}

A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then find the probability. \(P(6 \text { or king })\)

Three cards are drawn from a standard deck of cards. Find each probability. \(P(3 \text { hearts }),\) if no replacement occurs

An administrative assistant has 4 blue file folders, 3 red folders, and 3 yellow folders on her desk. Each folder contains different information, so two folders of the same color should be viewed as being different. She puts the file folders randomly in a box to be taken to a meeting. Find each probability. \(\begin{array}{|c|c|c|c|}\hline 0 & {1} & {2} & {3} \\ \hline \frac{1}{8} & {\frac{3}{8}} & {\frac{3}{8}} & {\frac{1}{8}} \\ \hline\end{array}\) \(P(H=2)\)

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. an arrangement of 4 blue tiles, 2 red tiles, and 3 black tiles in a row

For a college application, Macawi must select one of five topics on which to write a short essay. She must also select a different topic from the list for a longer essay. How many ways can she choose the topics for the two essays?

Determine whether each situation would produce a random sample. Write yes or no and explain your answer. pointing with your pencil at a class list with your eyes closed as a way to find a sample of students in your class

Lauren Wible of Bucknell University was the 2005 NCAA Division I women's softball batting leader with a batting average of .524. This means that the probability of her getting a hit in a given at-bat was \(0.524 .\) Find the probability of her getting exactly 2 hits in 4 at-bats.

GARDENING For Exercises 7 and \(8,\) use the following information. Dan is planting 24 irises in his front yard. The flowers he bought were a combination of two varieties, blue and white9. The flowers are not blooming yet, but Dan knows that the probability of having a blue flower is 75\(\% .\) What is the probability that at least 20 of the flowers will be blue?

For Exercises \(5-8,\) use the following information. The useful life of a certain car battery is normally distributed with a mean of \(100,000\) miles and a standard deviation of \(10,000\) miles. The company makes \(20,000\) batteries a month. What is the probability that if you buy a car battery at random, it will last between \(80,000\) and \(110,000\) miles?

Find the variance and standard deviation of each set of data to the nearest tenth. {2.4, 5.6, 1.9, 7.1, 4.3, 2.7, 4.6, 1.8, 2.4}

A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then find the probability. \(P(\text { queen or spade) }\)

Determine whether the events are independent or dependent. Then find the probability. A black die and a white die are rolled. What is the probability that a 3 shows on the black die and a 5 shows on the white die?

Determine whether each situation involves a permutation or a combination. Then find the number of possibilities. choosing 2 different pizza toppings from a list of 6

State whether the events are independent or dependent. choosing a president, vice-president, secretary, and treasurer for Student Council, assuming that a person can hold only one office

Determine whether each situation would produce a random sample. Write yes or no and explain your answer. putting the names of all seniors in a hat, then drawing names from the hat to select a sample of seniors

For Exercises \(9-14\) , use the following information. An exponential distribution has a mean of \(0.5 .\) Find each probability. $$ x>1.5 $$

Find each probability if a coin is tossed 5 times. \(P(5 \text { tails })\)

Find the variance and standard deviation of each set of data to the nearest tenth. {4.3, 6.4, 2.9, 3.1, 8.7, 2.8, 3.6, 1.9, 7.2}

School There are 8 girls and 8 boys on the Student Senate. Three of the students are seniors. What is the probability that a person selected from the student Senate is not a senior?

Determine whether the events are independent or dependent. Then find the probability. Yana has 4 black socks, 6 blue socks, and 8 white socks in his drawer. If he selects three socks at random with no replacement, what is the probability that he will first select a blue sock, then a black sock, and then another blue sock?

The Helping Hand Moving Company owns nine trucks. On one Saturday, the company has six customers who need help moving. In how many ways can a group of six trucks be selected from the company’s fleet?

Determine whether each situation would produce a random sample. Write yes or no and explain your answer. asking every twentieth person on a list of registered voters to determine which political candidate is favored

For Exercises \(9-14\) , use the following information. An exponential distribution has a mean of \(0.5 .\) Find each probability. $$ x>3 $$

Find each probability if a coin is tossed 5 times. \(P(0 \text { tails })\)

Find the variance and standard deviation of each set of data to the nearest tenth. {234, 345, 123, 368, 279, 876, 456, 235, 333, 444}

Two cards are drawn from a standard deck of cards. Find each probability if no replacement occurs. \(P(\text { two hearts })\)

Jesse has eight friends who have volunteered to help him with a school fundraise. Five are boys and 3 are girls. If he randomly selects 3 friends to help him, find each probability. \(P(2 \text { boys or } 2 \text { girls })\)

Bob is moving and all of his sports cards are mixed up in a box. Twelve cards are baseball, eight are football, and five are basketball. If he reaches in the box and selects them at random, find each probability. P(1 basketball, 2 football)

Six cards are drawn from a standard deck of cards. How many hands will contain three hearts and three spades?

State whether the events are independent or dependent. Each of six people guess the total number of points scored in a basketball game. Each person writes down his or her guess without telling what it is.

Determine whether each situation would produce a random sample. Write yes or no and explain your answer. finding the heights of all the boys on the varsity basketball team to determine the average height of all the boys in your school

For Exercises \(9-14\) , use the following information. An exponential distribution has a mean of \(0.5 .\) Find each probability. $$ x>\frac{1}{4} $$

Find each probability if a coin is tossed 5 times. \(P(\text { exactly } 2 \text { tails })\)

Find the variance and standard deviation of each set of data to the nearest tenth. {13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 67, 56, 34, 99, 44, 55}

Two cards are drawn from a standard deck of cards. Find each probability if no replacement occurs. \(P(\text { ace, then king })\)

Jesse has eight friends who have volunteered to help him with a school fundraise. Five are boys and 3 are girls. If he randomly selects 3 friends to help him, find each probability. \(P(\text { all boys or all girls) }\)

Bob is moving and all of his sports cards are mixed up in a box. Twelve cards are baseball, eight are football, and five are basketball. If he reaches in the box and selects them at random, find each probability. P(2 basketball, 1 baseball)

Evaluate each expression. \(P(8,2)\)

State whether the events are independent or dependent. The letters A through Z are written on pieces of paper and placed in a jar. Four of them are selected one after the other without replacing any of them.

For Exercises \(12-21,\) find the margin of sampling error to the nearest percent. $$ p=81 \%, n=100 $$

For Exercises \(9-14\) , use the following information. An exponential distribution has a mean of \(0.5 .\) Find each probability. $$ x<1 $$

Find each probability if a coin is tossed 5 times. \(P(\text { exactly } 1 \text { tail })\)

Stem \(\qquad\) Leaf 4 \(\qquad\) 4 5 6 7 7 5 \(\qquad\) 3 5 6 7 8 9 6 \(\qquad\) 7 7 8 9 9 9 \(\quad\) 4 \ 5 = 45

HEALTH For Exercises 12 and \(13,\) use the following information. The cholesterol level for adult males of a specific racial group is normally distributed with a mean of 4.8 and a standard deviation of \(0.6 .\) About what percent of the males have cholesterol below 4.2\(?\)

A die is rolled twice. Find each probability. \(P(2, \text { then } 3)\)

Jesse has eight friends who have volunteered to help him with a school fundraise. Five are boys and 3 are girls. If he randomly selects 3 friends to help him, find each probability. \(P(\text { at least } 2 \text { girls) }\)

Bob is moving and all of his sports cards are mixed up in a box. Twelve cards are baseball, eight are football, and five are basketball. If he reaches in the box and selects them at random, find each probability. P(1 football, 2 baseball)